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Michelson-Morley Experiment Question (No math)

In the experiment, Michelson was looking for a fringe shift, right? Would this fringe shift have been detectable AFTER the 90 degree rotation of the apparatus or only DURING the rotation?

I ask because it seems to me that the fringe patterns would be identical before and after the rotation, since for all practical purposes the two arrangements would be identical. It would only be DURING the rotation that the light pulses could interfere with each other in any detectable way.

You are correct. No shift was detected. That's why they call it the "most famous failed experiment". It was an attempt to measure the absolute speed of the Earth or the speed with respect to the aether. It turned out there is no such thing as absolute speed and no aether. Einstein's theory of relativity replaced all that.http://en.wikipedia.org/wiki/Michelson-Morely